Temperature determining device and process

ABSTRACT

The present invention relates to a totally novel device and process useful for the measurement of the temperature of a radiating body. More particularly, the present invention relates to a device that enhances the resolution and repeatability of the measured temperature of the radiating body by fitting a mathematical correlation to the emitted radiation spectra, generating calculated radiation intensities at specified wavelengths using the mathematical correlation, and then generating a suite of individual two-wavelength temperature values, which can be statistically evaluated and averaged for a final, measured temperature. In one embodiment, the device consists of an optical input system which receives a portion of the emitted radiation of a radiating body; a wavelength dispersion device which separates the emitted radiation according to wavelength; a radiation transducer which senses the separated radiation and provides an output corresponding to the respective wavelengths of the emitted radiation; means for generating a mathematical function to correlate the output of the radiation transducer to the corresponding wavelengths of incident radiation; and a means for generating a temperature value utilizing a form of the Planck Radiation Equation. Additionally, the present invention relates to the technique utilized to enhance the resolution and repeatability of the measured temperature.

FIELD OF THE INVENTION

The present invention relates to a radiation pyrometer useful for themeasurement of the temperature of a radiating body. More particularly,the present invention relates to a radiation pyrometer that enhances theresolution and repeatability of the measured temperature of theradiating body. Additionally, the present invention relates to thetechnique utilized to enhance the resolution and repeatability of themeasured temperature.

BACKGROUND OF THE INVENTION

Radiation pyrometers are known and commercially available. Typically,pyrometers are used to generate a measured temperature of a radiatingbody. The term "target" is used to indicate the radiating body evaluatedfor temperature determination, and the term "measured temperature" isused to indicate the value generated by a pyrometer or a pyrometrictechnique. The measured temperature may, or may not, be the actualtemperature of the target.

Pyrometers are particularly useful for measuring target temperatureswhen the target is positioned in a remote location, or when thetemperature or environment near the target is too hostile or severe topermit temperature measurement by other, more conventional, means orwhen the act of measuring in a contact manner may itself perturb thetarget temperature. The terms "measuring" and "measure" are use toinclude all aspects of a pyrometric technique including, but not limitedto, energy collection, correlation, data manipulation, the report of themeasured temperature, and the like.

Current pyrometers are one of two types: brightness or ratio devices.Brightness and ratio pyrometers both utilize a solution of a form of thePlanck Radiation Equation to calculate the target's measuredtemperature. The Planck Radiation Equation for spectral radiationemitted from an ideal blackbody is ##EQU1## where L.sub.λ =radiance inenergy per unit area per unit time per steradian per unit wavelengthinterval,

h=Planck's constant,

c=the speed of light,

λ=the wavelength of the radiation,

k_(B) =Boltzmann's constant, and

T=the absolute temperature.

For non-blackbodies, ##EQU2## where H.sub.λ =the radiation emitted, andε=emissivity. In the brightness method of pyrometry, H.sub.λ and ε aremeasured at a known wavelength, λ, and, therefore, T can be calculated.

Brightness devices rely upon capturing a known fraction of the radiationfrom a source in a particular solid angle. Brightness pyrometers knownin the prior art are dependent upon knowing the emissivity of thetarget, as required by Equation 2, supra. Emissivity is the ratio of theradiation emitted by the target to the radiation emitted by a perfectblackbody radiator at the same temperature. Typically, emissivity isunknown or estimated to a low degree of accuracy. Additionally, theemissivity is often a function of the target temperature, wavelength ofradiation examined, and history of the target. This limits the utilityof brightness pyrometry severely.

In practice, it is left to the user of a brightness pyrometer toestimate target emissivity, usually based upon an analysis of thetarget's composition. The user must then determine if the target'sthermal and environmental history have not appreciably altered thetarget emissivity. The wavelength or group of contiguous wavelengths ofradiation examined are determined by the instrument used, and noselection is possible. It is then left to the user to decide whether ornot the indicated target temperature is correct.

Brightness pyrometers are also susceptible to effects of theenvironment. The gases given off by the target or otherwise present inthe atmosphere can selectively absorb radiation at various wavelengths,thus altering the energy reaching the pyrometer and hence the measuredtemperature. Again, current instruments give no guidance or assistanceto the user in surmounting this obstacle.

Ratio pyrometers depend upon graybody behavior. A graybody is an energyradiator which has a blackbody energy distribution reduced by aconstant, known as the emissivity, throughout the wavelength intervalexamined. Ratio pyrometers detect the radiation intensity at two knownwavelengths and, utilizing Planck's Equation, calculate a temperaturethat correlates to the radiation intensity at the two specifiedwavelengths.

One form of the Planck Radiation Equation useful for ratio pyrometry isexpressed as ##EQU3## where T=absolute temperature; λ_(i) =specificwavelength chosen;

C'=second radiation constant=hc/k_(B) ;

R=ratio of radiation intensity at λ₁, to that at λ₂ ; and

K_(i) =instrument response factor at each wavelength chosen.

Here the low-temperature, short-wavelength approximation has been made;i.e., e^(hc/)λk_(B) ^(T) -1! has been replaced with e^(hc/)λk_(B) ^(T)!.

Tradeoffs must be made in the design of ratio pyrometers, particularlyin the wavelengths selected for inspection. Planck's Equation yieldshigher precision when the selected wavelengths are further apart.However, broadly spaced wavelengths permit extreme errors of indicatedtemperatures for materials that do not exhibit true graybody behavior.In practice, the two distinct wavelengths are typically chosen closetogether to minimize target emissivity variations, and the resultingdiminution of accuracy accepted as a limitation of the pyrometricdevice.

Ratio devices are also affected by gaseous absorptions from theworkpiece or environment. If a selective absorption occurs for either ofthe two wavelengths fixed by the instrument, the measured temperaturewill be incorrect.

Both brightness and ratio devices are therefore critically dependent ontarget emissivity and atmospheric absorptions in the region under study.

There is another, more subtle error to which both brightness and ratiodevices are prone. If the measuring device has a significant bandwidthat the wavelengths utilized, a simple emissivity correction will notsuffice for a target with spectral variation of emissivity. Theemissivity correction is treated as a variable gain for both classes ofdevices (brightness and ratio), and is therefore a linear correction. Ifthe bandwidth is large the contribution from neighboring wavelengths ofdifferent emissivity will render the resulting radiation intensityvariation with temperature non-linear, since the Planck function isnon-linear. This implies that there is no single emissivity correctionfor certain targets if the bandwidth is large. Furthermore, if anyelement in the optical path has a spectral transmission dependence, thesame error applies; no single gain factor can correct for such anoptical element (e.g., a gaseous, absorbing atmosphere, a glass windowor lens, a mirror, etc.).

Experimenters have investigated multi-wavelength pyrometry for sometime. G. A. Hornbeck (Temperature: Its Measurement and Control inScience and Industry, 3 (2), Reinhold, N.Y., 1962) described athree-wavelength device that could measure temperatures independent oftarget emissivity if the emissivity variation was linear over thewavelengths examined. The works of Cashdollar and Hertzberg(Temperature: Its Measurement and Control in Science and Industry, 5453-463, American Institute of Physics, New York, 1982; U.S. Pat. No.4,142,417) describe temperature measurement of particulate matter andgas in coal dust explosions using six-wavelength and three-wavelengthdevices utilizing a least squares fit to Planck's Radiation Equationunder the assumption that the particles are essentially graybodies andthat the dust cloud is optically thick.

Gardner et al. (High Temperature-High Pressures, 13, 459-466, 1981)consolidated the contents of a series of papers on the subject. Gardnerextends the concept of Hornbeck as well as the work of Svet (HighTemperature-High Pressures, 11, 117-118, 1979), which indicated thatemissivity could be modeled as linear over a range of wavelengths for anumber of materials. Also of interest is a previous publication byGardner (High Temperature-High Pressures, 12, 699-705, 1980), whichdiscusses coordinate spectral pairs of measured intensity and theassociated wavelength. Differences between all possible paircombinations are calculated, and the target emissivity estimated. Use ofthe emissivity with measured intensities permits calculation of thetarget temperature. The work of Andreic (Applied Optics, Vol. 27, No.19, 4073-4075, 1988) calculated the mean color temperature from manyspectral pairs and determined that detector noise of only 1% wouldproduce intolerable effects on measurement accuracy. The references ofHornbeck, Cashdollar, Hertzberg, Gardner, Svet, and Andreic, discussedabove, are incorporated herein by reference.

In contrast, the present invention measures the radiation intensity atnumerous wavelengths of extremely narrow bandwidth to generate a largenumber of coordinated data pairs of primary data points, fits theprimary data points to a mathematical function, generates astatistically significant number of processed data points from themathematical function, calculates an individual two-wavelengthtemperature for several pairs of processed data points, inspects theresults for internal consistency, and numerically averages theappropriate ensemble of individual two-wavelength temperatures togenerate the measured temperature. A data point is defined as awavelength and its associated (spectral)intensity such that if each weresubstituted into Equation 1 a unique temperature would result. Aprocessed data point is a data point as described above except that thespectral intensity is generated by the invention's mathematicalfunction. A pair of processed data points, hereafter known as agenerating pair, is required to generate a temperature by the use ofEquation 3, the formula for ratio pyrometry.

Nothing in the prior art envisions generating a non-Planckianmathematical function to fit primary data points, the calculation ofmultiple processed data points, and the numerical averaging of themultiple processed data points to generate a measured temperature ofextreme accuracy and precision with an associated tolerance. In contrastto the limited capabilities of previous techniques, the presentinvention has demonstrated an accuracy of measured temperature to ±5° C.at 2500° C., or ±0.15%, with a reproducibility of ±0.015%.

It also yields a tolerance--a measure of accuracy for the indicatedtemperature--which has never been offered before. It is an extremelyuseful feature, in that its result is that the user immediately knows towhat degree the measurement just made is to be relied upon. This is instark contrast with prior practice. The accuracy of pyrometers istypically specified by their manufacturers. This specification meansthat when the target is a blackbody (or possibly a graybody) and theenvironment does not interfere, the instrument will return a measurementof the specified accuracy.

But measurements of real interest occur with targets and environments ofunknown characteristics. The current invention detects whether thetarget or the environment are not well behaved. In the case of thetarget this can mean exhibiting other than graybody behavior; in thecase of the environment this might result from other than gray orneutral density absorption. In spite of such deficiencies, the presentinvention extracts the correct temperature. The tolerance reported withthe temperature indicates how successful that extraction was.

The present invention also has a unique advantage with respect toimmunity from noise. As has been previously described, one reason tochoose the wavelengths close together for ratio temperature measurementis to eliminate the variation of emissivity as a contributing factor tothe measurement error. The rationale is that if the wavelengths areclose together the change in emissivity is likely to be small. However,choosing the wavelengths close together maximizes the effect of noise.The magnitude of the noise generally remains constant throughout thespectrum. Choosing the wavelengths close together insures that theintensity will not differ much between the two wavelengths, thus makingthe noise contribution a larger fraction of the measured signal.

The invention overcomes this problem by using the weight of the entirespectrum collected to fix each processed-intensity data point. Thusprocessed data points can be chosen arbitrarily close together withoutmagnifying the noise contribution. Observation and modeling show thatthe contribution of noise is actually less than that expected fromevaluating the expression for error for the extremes of wavelengthmeasured. The error associated with any two wavelength/intensity pairscan be calculated using differential calculus if the error is small:##EQU4## where dR=error in the ratio, and R=ratio of intensities at twowavelengths.

Here the term dR/R can be replaced with the infinitesimal, ΔR/R, whereΔR is the error in the ratio, and similarly, dT/T can be replaced withΔT/T where ΔT is the error in temperature. The equation thus becomes:##EQU5##

Equation 5 can be used to calculate the maximum expected error, whichcan be compared to the error actually observed. The observed error ofthe invention has uniformly been smaller than the calculated value.Equation 5 further points out that the accuracy observed to date is notthe limit of the accuracy that can be expected. The invention iscalibrated according to a source of radiant intensity, instead of astandard source of temperature. Therefore, if the total error in radiantintensity, ΔR/R, is reduced to 1%, the expected error at 2500° C. is±0.10%.

If the target exhibits graybody behavior in any spectral region, it isalso possible for the present invention to quantify the targetemissivity in all regions. That is, the spectral emissivity for theentire wavelength range of the data can be quantified once thetemperature is known. Once quantified, changes in emissivity canidentify changes in the target as a function of various external effects(time, temperature, chemistry, etc.), as well as identify changes in thetarget environment, such as off-gassing, reactions, or materialdecomposition.

In addition, the choice of a source of radiance as the calibrationstandard extends the useful operating range of the present inventionwell above currently available temperature calibration standards.Current pyrometers are calibrated by exposing their optical inputs toblackbody sources at the temperature desired and in some fashion(electrical or mechanical) forcing the output of the pyrometer to agreewith the blackbody temperature. The limit for such a direct temperaturecalibration is 3000° C., the highest temperature a blackbody source cancurrently attain reproducibly. The invention described herein, by way ofcontrast, need only be calibrated by a source of radiant intensity (thatis, a device whose emitted radiation is known as a function ofwavelength, such as a standard lamp) to yield accurate temperatures.There is no need to expose the invention to the range of desiredtemperatures for it to be capable of measuring that range, a feature notpossible using the prior art.

SUMMARY OF THE INVENTION

The present invention is a method to measure the temperature of aradiating body, and a device which utilizes the method.

The measurement of temperature is a problem in many process industries:aluminum, iron and steel, ceramics, cement, glass, and composites are afew examples. Non-contact, and therefore non-perturbing, techniques ofradiation pyrometry would be preferred but for the weakness that, ascurrently practiced, they require knowledge of the target's emissivity.This parameter is defined as the ratio of the radiation emitted by thesample to that of a blackbody (ideal) radiator at the same temperature.

Unfortunately emissivity is a function of the target's composition,morphology, temperature, and mechanical and thermal histories, and ofthe wavelength at which the measurement is made. For some materials, itchanges while the temperature measurement is being made. Prior to thepresent invention, this central difficulty has proven so intractablethat the growth of radiation pyrometry has been stunted.

The effect of this difficulty is to preclude trustworthy temperaturedetermination without allowance for emissivity within the measurement.The historically recommended method of accomplishing this is to encasethe experiment in a blackbody cavity, thereby allowing the radiation tocome to thermal equilibrium. Clearly this is not a practical solution.

The commercially available technique of ratio, or two-color, pyrometryattempts another approach: canceling the emissivity by dividing twomeasurements of the radiation emitted and calculating the temperaturefrom this ratio. This works in principle but there is still no guaranteethat the emissivity is constant at the wavelengths chosen. This concernis the basis for the instrument maker's dilemma: whether to opt foremissivity cancellation or precision. Emissivity cancellation andprecision are mutually exclusive in a ratio instrument, and the choiceis signaled by the distance between wavelengths. The closer thewavelengths the more likely the emissivities are to cancel; the fartherapart the larger the magnitude of the resultant signal, and thus thegreater the precision.

The present invention, which is suitable for measuring the temperatureof any radiating body that is above ambient temperature, quantifiesradiation intensity at multiple wavelengths, generates a mathematicalfunction to fit the primary data points, calculates multiple processeddata points using the mathematical function, utilizes multiple pairs ofthe processed data points to calculate individual two-wavelengthtemperature estimates, inspects the results for internal consistency,and numerically averages the estimates to generate a measuredtemperature of great accuracy and a tolerance, which is a quantificationof that accuracy. The invention also permits evaluation of the qualityof the emission spectra being measured, and identifies whether thetarget exhibits true graybody behavior and, if it does not, whichportions of the spectra will generate erroneous measured temperatures.

The present invention's ability to quantify radiation intensities atmultiple wavelengths with a single sensor minimizes temperaturemeasurement errors due to variations between sensors. Removing thissource of intrinsic error permits statistical manipulation of thecollected data to enhance the accuracy and reproducibility of thetemperature measurement technique. Fitting the primary data points to amathematical function accommodates target deviations from true graybodybehavior, as well as further minimizing the effects of thermal,detector, and instrument noise.

The present invention provides a process for measuring temperature,comprising quantifying the radiation intensity emitted by a radiatingbody at no less than 4 distinct wavelengths; generating a mathematicalfunction which correlates the radiation intensities to the correspondingwavelength at which the radiation intensity was quantified; andgenerating a temperature value utilizing Equation 3 and no less than twoprocessed data points generated utilizing the mathematical function. Theinvention may also be practiced using three or more processed datapoints generated utilizing the mathematical function. The invention alsoencompasses the use of only quantified radiation intensity whichexhibits emission spectra consistent with known thermal radiationeffects for generation of the mathematical function. Data may be said tobe consistent when the processed data points are computed at wavelengthswhere the fractional residuals of the quantified radiation intensityexhibit an RMS value substantially equal to zero or where the quantifiedradiation intensity exhibits magnitudes of fractional residuals no lessthan -0.1 and no more than 0.1, preferably no less than -0.05 and nomore than 0.05, most preferably no less than -0.02 and no more than0.02. The invention may also be used to determine the emissivity of theradiating body, as well as the absorption of the intervening environmentbetween the radiating body and the device utilized to quantify theradiation intensity of the body. Additionally, the chemical speciespresent in the environment between the radiating body and quantifyingdevice may be identified and measured.

The invention also includes averaging the individual temperature valuescalculated utilizing Equation 3 and no less than three processed datapoints, and the determination of the tolerance of the resultingtemperature value by calculating the statistical variation of thetemperature values calculated utilizing Equation 3 and no less thanthree generating pairs. One pertinent statistical variation is thedetermination of the standard deviation of the average of the individualtemperature values calculated.

The invention also encompasses a device, comprising an optical inputsystem, a wavelength dispersion device, a radiation transducer, a meansfor generating a mathematical function to correlate the radiationtransducer output to the corresponding wavelengths of incidentradiation; and a means for generating a temperature value utilizingEquation 3 and no less than two processed data points generatedutilizing the mathematical function, as well as all the othercapabilities described herein.

The present invention thus provides a process and apparatus fortemperature determination which exhibits improved accuracy, noiseimmunity, great adaptability to varied temperature measurementsituations, and unlimited high temperature response. In addition, thetolerance of the measured temperature is reported, temperaturemeasurements are made independent of knowledge of the target emissivity,and all corrections are made digitally (in a mathematical expression,leaving the hardware completely versatile). These features provide amethod and device which are effective in non-ideal, i.e., absorbing orreflecting, environments.

Other advantages will be set forth in the description which follows andwill, in part, be obvious from the description, or may be learned bypractice of the invention. The advantages of the invention may berealized and attained by means of the instrumentalities and combinationsparticularly pointed out in the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 A conceptual schematic of the invention

FIG. 2 A graph of the data and of the mathematical function (anintermediate output of the invention) for 2000° C.

FIG. 3 Fractional residuals for the mathematical function of FIG. 2,with systematic variations less than 0.02

FIG. 4 An example of a graph of noisy data with a graph of themathematical function generated by the invention superimposed

FIG. 5 A graph of the fractional residuals for a random noise testillustrating fractional residuals with an RMS value of zero orsubstantially zero

FIG. 6 Data collected by the invention and corrected for instrumentresponse

FIG. 7 The data of FIG. 6 with 10% random noise added

FIG. 8 Spectral data collected by the invention in an off-gassingenvironment, corrected for instrument response

FIG. 9 Spectral data collected immediately after FIG. 8 but with theenvironmental off-gas purged away

FIG. 10 Absorption spectra of chemical species present in the targetenvironment

DETAILED DESCRIPTION OF THE INVENTION

The invention relates to a non-perturbing method for the measurement ofelevated temperatures, and an apparatus to utilize the method.

The method of the instant invention includes the measurement of thermalradiation at multiple wavelengths, representing the measurements ofthermal radiation by an analytical function, determining the usefulrange of wavelengths used for thermal radiation measurement, and testingcalculated temperatures based upon multiple pairs of measured thermalradiation for consensus. Additional steps of calibrating the apparatusfor system optical response, and for displaying the calculated consensustemperature, or activating a device based upon the calculated consensustemperature, are also encompassed by the invention.

The apparatus of the invention is any device, or collection of devices,which is capable of separating thermal radiation into its spectralcomponents, transducing the spectral components at three or morewavelengths, generating an analytical function to represent thetransduced radiation, determining the range of the analytical functionwhere the transduced radiation is within a specified tolerance, andcalculating a consensus temperature based upon two or more points on thegenerated analytical function.

Reference will now be made to the preferred embodiment of the apparatus,an example of which is illustrated schematically in FIG. 1. Asillustrated in the figure, the apparatus of the invention comprises anoptical input, an optical transducer, and computation means.

Several embodiments of the optical input system have been utilized. Apreferred embodiment utilized a commercially available camera body, inthis case a Nikon F3. Thus, any appropriate compatible lens can be used.Specifically, a Tamron SP 28-135 mm F/4 zoom lens was utilized.

The back of the camera was modified to accept a fiber optic connectorthat held the end of a fiber optic cable at a location corresponding toboth the center of the focusing reticule and the film plane. Depicted asthe Optical Transmission Line in FIG. 1, the fiber optic cable is usedto couple the optical input system with the optical transducer.

The target could thus be observed through the camera viewfinder and theappropriate portion of the target brought into focus in the traditionalmanner. The camera shutter was then locked open to transfer the incomingradiation to the pyrometer. The fiber optic cable was PCS 1000, aplastic-clad single-strand fiber with a 1-mm fused-silica core,manufactured by Quartz and Silice and available from Quartz Products,P.O. Box 1347, 688 Somerset St., Plainfield, N.J. 07060. As is clear toone skilled in the art, numerous methods and devices capable ofdirecting thermal radiation to the transducer are encompassed by theinvention, including but not limited to lenses, mirrors, prisms,graded-index fiber optics, holographic and replicated optical elements,electrical and magnetic equivalents of lenses and mirrors, directradiation, and the like.

The second end of the fiber optic cable terminated in a flat-fieldspectrograph which dispersed the light into its spectral components. Thespectrograph used in the preferred embodiment, model CP-200 manufacturedby Instruments SA (of 6 Olsen Ave., Edison, N.J. 08820-2419), was fittedwith a concave holographic grating of either 75 or 200 lines/mm whichprovided dispersion of 0.9 or 0.6 nm, respectively, when coupled with amodel 1462 detector manufactured by EG&G Princeton Applied Research,P.O. Box 2565, Princeton, N.J. 08543-2565. The model 1462 detector is alinear diode array with 1024 elements on 25 μm spacing. An typicalorder-sorting blocking filter limits the spectrum to wavelengths longerthan 400 or 500 nm.

The flat field spectrograph and linear diode array comprise theradiation transducer of the preferred embodiment. The present inventionencompasses any means for transducing the spectral components of thethermal radiation into a signal which may be used to generate ananalytical function to represent the radiation. The transduced signalcould be pneumatic, hydraulic, optical, acoustic or gravimetric, but ismore typically electrical. Other acceptable transducers include, but arenot limited to, linear diode arrays, charge coupled devices, chargeinjection devices, infrared focal plane arrays, multiple photocellarrays, and single element detectors equipped with multiple wavelengthfilters, absorbers, or optical systems capable of separating thespectral radiation.

In the preferred embodiment, the transducer generates an analogelectrical signal, which is converted to an equivalent digital signal bya PARC Model 146 OMA A/D converter.

The digitized signal thus resulting quantifies the thermal radiationintensity at 1024 discrete wavelengths (collected simultaneously througha common optical system) and is stored numerically in a computer filefor post-processing.

Correction (intensity calibration) of the digitized data so that thediscrete spectral intensities have the appropriate relative magnituderequires a system response curve. This is generated separately bycollecting data using a standard lamp as the target. The resultingsystem response curve provides correction through a matrixmultiplication of subsequent measurements, and need not be repeatedunless apparatus components are reconfigured.

This calibration of the system was effected using a standard of spectralirradiance, such as an Eppley Laboratories 100 watt Quartz Iodine lamp.From Equation 5, ##EQU6## it can be seen that, for typical values oftemperature and wavelength, the error in temperature is significantlysmaller than the error in the irradiance calibration. For example, if a1% irradiance calibration were utilized to calibrate a system atwavelengths 550 and 900 nanometers the resulting error in temperature at1000 K. would be 0.1%, or 1 degree.

The corrected digitized data are then represented analytically byfitting these data to a mathematical function. It has been found thatseveral non-Planckian mathematical expressions can represent thermalradiation well: exponential and logarithmic functions, and polynomialsof second, third, fourth, and higher orders. In the case of thequadratic and higher order polynomials the method of orthogonalpolynomials can be used. FIG. 2 shows a corrected data set and the fitof that set on the same axes.

If every combination of two wavelength intensities were used tocalculate the target temperature, more than 500,000 calculations oftemperature would be performed. While this can be easily done usingcurrently available microcomputers, it is neither necessary nordesirable. Better results are obtained when an analytical function isused to represent the data, and subsequent calculations use theanalytical form.

As described in Equation 1, above, a general statement of The PlanckRadiation Equation for spectral radiation emitted from an idealblackbody is ##EQU7## Defining the radiation constants C and C' by theexpressions

    C=2hc.sup.2, and C'=hc/k.sub.B,

Equation 1 can be manipulated to read ##EQU8## where the usual shortwavelength assumption has been made. The temperature can then becalculated using the expression ##EQU9## where the ratio of spectralintensities, ^(L) λ₁ ^(/L) λ₂ is represented as R. This solution is thebasis of all ratio, or two-color, pyrometry.

Differentiation of this expression to evaluate the error in thecalculated temperature (dT/T) yields Equation 4, ##EQU10## The error inthe calculated temperature is thus a product of three terms. The firstterm, T/C', is fixed by the target temperature and the radiationconstant. The third term, the uncertainty in the ratio of spectralintensities dR/R, is a function of the specific equipment used tomeasure target spectral intensity. Inspection of Equation 4 indicatesthat the uncertainty in temperature, dT/T, is directly proportional tothe second term, (λ₂ ×λ₁)/(λ₁ -λ₂) which is known as the effectivewavelength.

Rearranging the expression for effective wavelength in Equation 4 leadsto ##EQU11## where λ₂ <λ₁. Inspection of this expression of theeffective wavelength term indicates that the expression is minimizedwhere λ₂ is as small as possible, and λ₁ is as large as possible.

Use of Expert System Software

The use of specialized software, known generally as "expert systemsoftware" is applicable to the present invention. The expert systemsoftware performs, among other functions, the following:

Collects data

Corrects data for background and for instrument, environment, and target(if known) optical response

Discards obviously non-thermal data

Represents data by an analytical function

Determines the useful spectral range of the data

Tests the data for consensus temperature

Either

a) Uses the consensus range to report the temperature and its tolerance

b) Reports that there is no consensus.

Thus, the invention provides a measured temperature and quantifies theaccuracy of the result obtained by a statistical evaluation of theresultant suite of calculated temperatures.

The invention also identifies those situations when the process andapparatus of the invention are unsuccessful. This typically means thatsome environmental parameter is perturbing the data. In this event,suitable optics can be utilized, due to the extreme flexibility of theapparatus, to selectively filter, remove or compensate for theperturbing effect. Additionally, portions of the emission spectra thatexhibit behavior inconsistent with known thermal radiation effects canbe excised from the evaluated data set, and erroneous measurements basedupon inconsistent segments of the evaluated spectra can be avoided.

FIG. 6 depicts a collection of raw emissivity data points, and clearlyshows absorption bands at 590 nm, 670 nm and at 770 nm. These excursionsare non-thermal, systematic errors. Although the present inventionminimizes the effect of such excursions, excising the non-thermal dataor selecting intensity values from portions of the data not affected bythe non-thermal error can enhance the quality of the temperaturedetermination and increase the accuracy of the measurement.

The invention may also maintain a database of previous temperaturemeasurements for a specific target. Subsequent temperature measurementsof the same or similar targets may be compared to the software'sdatabase values to provide an internal check of the data.Emissivity/wavelength relationships, in particular, may be thuscritically evaluated.

Except for the collection of raw data points, generating a mathematicalfunction to fit the data points, the calculation of individualtwo-wavelength calculated temperatures, the numerical averaging of theindividual two-wavelength calculated temperatures to generate a measuredtemperature, and the discarding of values not meeting the statisticalcriteria chosen, the specifics related to measuring target temperaturesare not, however, critical to the present invention.

EXAMPLE 1

A series of temperature measurements were made using two commerciallyavailable NIST-traceable blackbodies as targets. The high temperaturesource was Model BWS156A (Electro Optical Industries Inc., P.O. Box3770, Santa Barbara, Calif. 93130), covering the range from 1000° C. to3000° C. The low temperature source was Model 463/101C (InfraredIndustries, 12151 Research Parkway, Orlando, Fla. 32826), covering therange from 100° C. to 1000° C. Blackbody setpoints from 600° C. to 3000°C. were evaluated using the invention. Table 1 is an example of such anevaluation. In general, two measurements were made at each setpoint;these show the exceptional reproducibility of the invention.

The sequence of operation of the invention began with the collection ofraw data. The optical input portion of the apparatus was positioned topermit the radiation emitted from the target to be directed onto thesensor, and the spectral emissions were quantified at multiplewavelengths.

The first computational step was that the background was subtracted fromthe raw data. It had been collected in the same manner as the raw data,but without the target's radiation being presented to the optical input.The background is typically electronic in nature (e.g., dark current)but may have a physical component: either reflections or emissions.

The next step was the correction of the data for instrument factors:i.e., transmittivity/reflectivity of every optical element in thecollection and transmission path and adjustment for the variousresponsivities of the individual detector elements. The corrected datawas then fitted to a numerical expression, such as a polynomial ofhigh-enough order (quadratic or higher), to adequately represent thedata. A cubic expression was determined to be adequate. An example ofthe fit of the numerical expression to raw data points from Example 1,an evaluation at 2000° C., is depicted in FIG. 2.

The residuals (data values of intensity subtracted from correspondingvalues from fitted curve) are helpful in quantifying the accuracy of anevaluation. The fractional residuals (residual divided by correspondingdata value) from the 2000° C. fit selected above are depicted in FIG. 3.Inspection of FIG. 3 indicates that fractional residuals with asystematic error less than 0.02 may be found between 500 nm and 800 nm.This boundary of ±0.02 has been found to be a useful criterion as towhether or not the data is well represented by the analytical functionwhere systematic variations from zero are seen in the fractionalresiduals. Where the fractional residuals show variations of a randomnature, i.e., their RMS value is zero, there appears to be no upperlimit to their magnitude for good results to be obtained. Therefore, theportion of the data between 500 and 800 nm was selected as the usefulrange of the evaluation.

Another measure of the quality of the analytical representation of thedata is the coefficient of determination. Coefficients of determinationsuch as that shown in Table 6, greater than 0.99, are often observed.While this indicates that the data are well-represented by theanalytical function, the reverse is not true. For example, thecoefficient of determination for Table 7 is 0.910.

The numerical expression that had been fitted to the data must thensolved for 6-50 values of intensity of radiation for a series ofwavelengths chosen incrementally. The increment is usually 25 or 50nanometers, and the range over which they are chosen is determined bythe temperature of the object. These are the pairs from which thetemperatures are calculated. The number of individual temperaturevalues, N, is j items taken 2 at a time, _(j) C₂ or ##EQU12## For thisexample, j=6, and 15 intensity pairs were used to generate 15 individualtemperature values.

These values were then inspected for consensus; i.e., to see whether ornot they yielded the same temperature. Since the entire spectrum isutilized in a systematic way, it is possible to determine from thisinspection which areas of the collected spectrum yield values which arein general agreement with each other. In this way absorptions andemissions from the optical environment as well as non-graybody areas ofthe target spectrum can be eliminated, and the previous steps repeateduntil an acceptable consensus temperature is determined, or it isdetermined that the apparatus, as configured, is not capable ofgenerating a consensus temperature within the acceptable errortolerance.

The consensus temperature is judged worthy of reporting as the objecttemperature if a significant portion of the spectrum yields a consensusvalue which, when averaged, displays a standard deviation within anacceptable tolerance range, typically of on the order of 0.25% of theabsolute temperature. A significant body of experience using standardsof known temperature as the objects to be measured indicates that thestandard deviation of the consensus temperature can be considered as thetolerance to which the temperature is known.

EXAMPLE 2-4

Multiple temperature evaluations were made in the manner described inExample 1 of blackbody targets at temperatures between 850° C. and 2500°C. The results are reported in Tables 2-4.

EXAMPLE 5

Evaluation of the error correcting capability of the invention wasaccomplished by intentionally injecting random error (noise) into bothgenerated (artificial) and real data sets, but otherwise practicing thealgorithm of the invention as described above.

Tables of spectral intensities at various wavelengths for varioustemperatures were generated using Planck's law for a number oftemperatures. These data then had varying amounts of error inserted overtheir spectral ranges using a random number generator. Specifically,error of ±10% was added from 450-495 nm, ±5% for 496-517 nm, and ±2% for518-800 nm. FIG. 4 depicts the resulting intensity/wavelength curve for2400 Kelvins and the fitted curve for the same region. FIG. 5 depictsthe fractional residual values resulting from a cubic curve fit to theartificially noisy raw data. The residual evaluation for this exampleclearly shows the noise added. The results of this and other artificialrandom noise tests are tabulated in Table 5. Inspection of this tableshows the invention returns a value closer to the temperature used togenerate the uncorrupted spectra than that returned by simplemulti-value averaging; the average error of the invention is less thanhalf that of simple averaging methods.

To extend the noise evaluation to real data, error was injected to realdata sets selected randomly. FIG. 6 depicts the selected raw datacorrected for instrument response. A total of 21 calculations oftemperature were made using points extracted from the fitted curve atvalues from 625 to 925 nm, in 50 nm increments (j=7; N=21). The reportedtemperature, shown as "Prediction Results" and a tabulation of the 21pairs is included as Table 6. An average temperature of 3160.0 Kelvinswas generated, with a tolerance of ±10.3 Kelvins.

Random error was then added to the data of FIG. 6; a random numbergenerator added a maximum error of ±10% to each value of intensity. FIG.7 depicts the data with the error added. A cubic expression was then fitto the corrupted data, and the same 21 pairs of intensities as in theoriginal data were evaluated. As shown in Table 7, the present inventionreported a temperature of 3172.7 ±23.2 Kelvins. The indicatedtemperature has changed by 12.2 Kelvins, and the measurement tolerancehas increased 12.9 Kelvins. The difference in the temperaturecalculation has changed less than 0.4% (12.2/3160) while the data hasbeen corrupted by 10%. Moreover, the increase in the measurementtolerance is seen to match almost exactly the change in the reportedtemperature due to the injected noise (do we need the quotes?). Thisshows that the tolerance identifies to the user the degree of error inthe reported value.

Comparative Example 5(a)

The corrupted data of Example 5, i.e., the data shown in FIG. 7, wereevaluated without fitting the data to a mathematical expression. Thedata point closest to the selected wavelength values (624.4006 nm for"625") were chosen for the temperature calculation.

Table 8 shows that the temperature calculated in the manner of the priorart would change 162 Kelvins, to 3322.0 Kelvins, for a noise-inducederror of greater than 5%. The measurement tolerance also increaseddramatically, to ±439 Kelvins, indicating that the temperature is nolonger well known.

EXAMPLE 6

Example 6 illustrates both the ability of the invention to determine thetemperature despite interference by absorbing gas and its ability toaccurately determine temperatures much greater than 3000° C. FIG. 8shows spectral data collected from a target in an off-gassingenvironment with a minimal clearing flow of purge gas. Table 9 shows thetemperature calculation performed by the invention for this data. FIG. 9shows a data collection immediately after that of FIG. 8 with allparameters held constant except for the purge, which had been increasedby a factor of six. The absorbing gas had been mostly cleared away andthe only absorptions left are the narrow ones at 589 and 767 nanometers.Table 10 is the temperature calculation for these data. As can be seen,the temperatures indicated by both calculations, 3526.7 Kelvins/3253.7°C. for Table 9 and 3519.4 Kelvins/3246.4° C. for Table 10, agree verywell showing that the invention operates successfully in the presence ofabsorbing gas. These also show that the invention is capable offunctioning as described well above 3000° C./3273 Kelvins.

EXAMPLE 7

Example 7 illustrates the ability of the invention to provideidentification of absorbing chemical species in the environment. A dataensemble such as that represented by the graph of FIG. 8 is the startingpoint. The invention's output temperature is calculated as has beendescribed. This value of temperature is then substituted into Equation 1to generate a corresponding Planckian intensity for every wavelength ofthe data set. The generated intensity is then normalized to thecollected data at a point where no non-thermal effects are present (inthis case at 800 nanometers). The difference between these two sets ofspectral intensities is then calculated, as in FIG. 10, and is theabsorption spectrum of the chemical species present. These can beidentified using standard tables of chemical spectra. The net effect isthat two unknowns, the temperature of the target and the chemicalspecies of the intervening environment, have been quantified by onemeasurement.

Thus, it should be apparent to those skilled in the art that the subjectinvention accomplishes the objects set forth above. It is to beunderstood that the subject invention is not to be limited by theexamples set forth herein. These have been provided merely todemonstrate operability, and the selection of specific components andoperating methodologies, if any, can be determined from the totalspecification disclosure provided, without departing from the spirit ofthe invention herein disclosed and described, the scope of the inventionincluding modifications and variations that fall within the scope of theattached claims.

                  TABLE 1                                                         ______________________________________                                        All values in Degrees C.                                                              Temperature                                                           Setpoint                                                                              Indicated      Difference                                                                             Tolerance                                     ______________________________________                                        1600    1603.3         3.3      8.17                                                  1603.3         3.3                                                    1700    1700.3         .3       8.38                                                  1700.4         .4       8.37                                          1800    1798.2         -1.8     7.92                                                  1798.4         -1.6     7.92                                          1900    1897.8         -2.2     7.14                                                  1897.8         -2.2     7.14                                          2000    2001.5         1.5      7.98                                                  2001.5         1.5      8.07                                          2100    2106.1         6.1      6.45                                                  2106.1         6.1      6.45                                          2200    2198.1         -1.9     6.96                                                  2198.2         -1.8     6.90                                          ______________________________________                                    

                  TABLE 2                                                         ______________________________________                                        All temperatures in Deg C.                                                            Temperature                                                           Setpoint                                                                              Indicated      Difference                                                                             Tolerance                                     ______________________________________                                        850     855.3          5.3      15.21                                                 851.4          1.4      14.73                                                 852.6          2.6      14.76                                                 857.9          7.9      15.54                                                 848.2          -1.8     15.05                                                 850.6          0.6      15.02                                         900     899.0          -1.0     6.71                                                  898.3          -1.7     6.90                                                  900.7          .7       6.36                                                  898.2          -1.8     6.85                                                  898.3          -1.7     7.43                                          1000    998.3          -1.7     2.90                                                  1002.6         2.6      2.92                                                  1000.5         .5       3.44                                                  1002.4         2.4      2.86                                                  1001.8         1.8      2.95                                          ______________________________________                                    

                  TABLE 3                                                         ______________________________________                                        All temperatures in Deg C.                                                            Temperature                                                           Setpoint                                                                              Indicated      Difference                                                                             Tolerance                                     ______________________________________                                        1300    1302.9         2.9       6.54                                         1400    1397.6         -2.4     10.2                                          1500    1501.4         1.4      11.8                                          1650    1649.9         -0.1     10.4                                          ______________________________________                                    

                  TABLE 4                                                         ______________________________________                                        All temperatures in Deg C.                                                            Temperature                                                           Setpoint                                                                              Indicated      Difference                                                                             Tolerance                                     ______________________________________                                        1600    1601.6           1.6    5.79                                          1800    1797.2         -2.8     6.29                                                  1797.2         -2.8     6.24                                          2000    1999.0         -1.0     5.05                                                  1999.0         -1.0     5.05                                          2200    2195.6         -4.4     3.80                                                  2195.7         -4.3     3.80                                          2300    2296.7         -3.3     1.21                                                   2299.5*       -0.5     5.96                                          2500    2494.9         -5.1     2.66                                                   2498.0*       -2.0     5.78                                          ______________________________________                                         *Difference in repeatability is due to change in apertures between            measurements.                                                            

                  TABLE 5                                                         ______________________________________                                        Random Noise Tests                                                            Generating                                                                             Invention Difference                                                                              Average Difference                               Temperature                                                                            Temperature                                                                             (Col B-   Temperature                                                                           (Col D-                                  Column A Column B  Col A)    Column D                                                                              Col A)                                   ______________________________________                                        2250     2250.1    0.1       2254.3  4.3                                      2400     2398.5    -1.5      2397.9  -2.1                                     2500     2502.5    2.5       2504.6  4.6                                      2600     2601.5    1.5       2604.5  4.5                                      2700     2705.3    5.3       2708.3  8.3                                      ______________________________________                                    

                  TABLE 6                                                         ______________________________________                                        Prediction Results Temp = 3160.0 Tol = 10.3 N = 21 r.sup.2 = .99063           675        725      775    825    875  925                                    ______________________________________                                        625     3140   3155     3160 3160   3159 3156                                 675            3173     3174 3170   3165 3162                                 725                     3174 3168   3163 3158                                 775                          3162   3156 3151                                 825                                 3149 3144                                 875                                      3138                                 ______________________________________                                         Data File: f3213m2.dat                                                   

                  TABLE 7                                                         ______________________________________                                        Prediction Results Temp = 3172.7 Tol = 23.2 N = 21. r.sup.2 = .91024          675        725      775    825    875  925                                    ______________________________________                                        625     3146   3168     3177 3180   3175 3167                                 675            3195     3198 3194   3186 3173                                 725                     3201 3194   3183 3166                                 775                          3186   3170 3152                                 825                                 3154 3132                                 875                                      3108                                 ______________________________________                                         Data File: F3213M2R.TXT                                                  

                  TABLE 8                                                         ______________________________________                                        Prediction Results Temp = 3322.0 Tol = 439. N = 21.                           675        725      775    825    875  925                                    ______________________________________                                        625     3030   2898     3242 3092   3164 3240                                 675            2758     3393 3120   3214 3310                                 725                     4619 3391   3462 3555                                 775                          2603   3009 3235                                 825                                 3646 3789                                 875                                      3971                                 ______________________________________                                         Data File: F3213M2R.TXT                                                  

                  TABLE 9                                                         ______________________________________                                        Prediction Results Temp = 3526.7 Tol = 45.3 N = 28. r.sup.2 = .98044          575      625     675     725   775   825   875                                ______________________________________                                        525  3377    3442    3477  3495  3505  3506  3502                             575          3521    3544  3553  3554  3549  3539                             625                  3571  3574  3569  3560  3545                             675                        3576  3568  3554  3536                             725                              3558  3542  3519                             775                                    3522  3495                             825                                          3464                             ______________________________________                                         Data File:f3 220m2.und                                                   

                  TABLE 10                                                        ______________________________________                                        Prediction Results Temp = 3519.4 Tol = 20.9 N = 21. r.sup.2 = .97263          600        650      700    750    800  850                                    ______________________________________                                        550     3556   3553     3543 3533   3527 3525                                 600            3549     3535 3524   3517 3516                                 650                     3520 3507   3501 3504                                 700                          3493   3490 3496                                 750                                 3486 3498                                 800                                      3513                                 ______________________________________                                         DataFile: f3221m2.und                                                    

I claim:
 1. A process for determining the temperature of a radiatingbody, comprising:a) quantifying the radiation intensity emitted by aradiating body at no less than 4 distinct wavelengths; b) generating amathematical function which represents said quantified radiationintensities at the corresponding wavelength at which said radiationintensity was quantified; c) selecting no less than two specificwavelengths; d) generating a spectral intensity using said mathematicalfunction for each of said wavelengths; and e) determining an individualtwo-wavelength temperature value of said radiating body utilizing theradiation equation ##EQU13## where T₁₂ =individual two-wavelengthtemperature, λ₁. λ₂, . . . λ_(n) =specific wavelengthsselected,C'=second radiation constant, and R=ratio of the generatedspectral intensity I₁, calculated using said mathematical function atλ₁, to the generated spectral intensity I₂, calculated using saidmathematical function at λ₂.
 2. The process of claim 1, wherein saidselection step comprises selecting no less than three specificwavelengths; and wherein said determining an individual two-wavelengthtemperature value step comprises determining an individualtwo-wavelength temperature value of said radiating body utilizing saidradiation equation for each pair of said specific wavelengths selectedand said spectral intensity generated utilizing each of said specificwavelengths.
 3. The process of claim 2, wherein only said quantifiedradiation intensity which exhibits emission spectra consistent withknown thermal radiation effects is utilized for generation of saidmathematical function.
 4. The process of claim 2, wherein said generatedspectral intensities are utilized to determine said two-wavelengthtemperatures at wavelengths at which said quantified radiationintensities exhibit fractional residuals no less than -0.1 and no morethan 0.1.
 5. The process of claim 2, wherein said generated spectralintensities are utilized to determine said two-wavelength temperaturesat wavelengths at which the fractional residuals of said quantifiedradiation intensities exhibit an RMS value substantially equal to zero.6. The process of claim 2, wherein an average temperature value isdetermined by the averaging of said individual two-wavelengthtemperature values determined for every pair of said specificwavelengths and said spectral intensities.
 7. A process for determiningthe spectral emissivity of a radiating body, comprisinga) determiningthe temperature according to claim 6, and b) calculating said spectralemissivity using the expression ##EQU14## where λ=one of said distinctwavelengths at which the radiation intensity is quantified H.sub.λ =theradiation quantified at wavelength λ, ε=the emissivity, T=saiddetermined temperature, h=Planck's constant, c=the speed of light, andk_(B) =Boltzmann's constant.
 8. A process for measuring the tolerance ofthe measured temperature of a radiating body, comprisinga) determiningthe temperature according to claim 6, and b) calculating the statisticalvariation of said individual two-wavelength temperature valuesdetermined utilizing said radiation equation, said no less than threespecific wavelengths, and said spectral intensities generated utilizingeach of said specific wavelengths.
 9. The process of claim 8, whereinsaid statistical variation is the standard deviation of said averagetemperature value.
 10. A temperature determining device, comprising:a)an optical input system which receives a portion of the emittedradiation of a radiating body; b) a wavelength dispersion device whichseparates said emitted radiation according to wavelength; c) atransducer which senses said separated radiation and provides aquantified output corresponding to radiation intensity for eachwavelength of said emitted radiation; d) means for generating amathematical function to represent said quantified output of saidradiation transducer as a function of wavelengths; e) means forselecting no less than two specific wavelengths; f) means for generatinga spectral intensity value at each of said selected specificwavelengths, utilizing said mathematical function; and g) means fordetermining an individual two-wavelength temperature value utilizing noless than two of said spectral intensity values and the radiationequation ##EQU15## where T₁₂ =individual two-wavelength temperature, λ₁.λ₂, . . . λ_(n) =specific wavelengths selected,C'=second radiationconstant, and R=ratio of the generated spectral intensity I₁, calculatedusing said mathematical function at λ₁, to the generated spectralintensity I₂, calculated using said mathematical function at λ₂.
 11. Thedevice of claim 10, wherein said means for determining an individualtwo-wavelength temperature value comprises means for determining atwo-wavelength temperature value of said radiating body utilizing saidradiation equation for each pair of no less than three specificwavelengths and their corresponding spectral intensities generatedutilizing said mathematical function.
 12. The device of claim 11,wherein only said quantified output corresponding to radiation intensitywhich exhibits emission spectra consistent with known thermal radiationeffects is utilized for generation of said mathematical function. 13.The device of claim 11, wherein said spectral intensities are generatedat wavelengths at which said quantified output corresponding toradiation intensity exhibits fractional residuals no less than -0.1 andno more than 0.1.
 14. The device of claim 11, wherein said spectralintensities are generated at wavelengths at which the fractionalresiduals of said quantified output corresponding to radiation intensityexhibit an RMS value substantially equal to zero.
 15. The device ofclaim 11, wherein a average temperature value is the average of saidtwo-wavelength temperature values determined utilizing said radiationequation.
 16. The device of claim 15, further comprising thedetermination of the tolerance of said average temperature value bycalculating the statistical variation of said two-wavelength temperaturevalues.
 17. The device of claim 16, wherein said statistical variationis the standard deviation of said average.